Like 2stroke said, you have to make sure you have spark. There are testers available. The dangerous way to test is remove the plug from the cylinder, plug it back in the wire, lay it against conductive metal on the engine, pull the rope and the plug should spark bright blue. Keep in mind you are making sparks while the engine is emitting gas, so it would be wise to take it outside to do this test. If it's red or weak, you need to clean the points. This will not test the plug under pressure, so it doesn't thoroughly test the system.
Have you measured the compression? Every saw is different, but they get hard to start under 120psi. 90psi will still "feel" like your have compression, but will probably never start.
If you have compression, spark, then it's back to what I said about the carburetor. The inlet needle is stuck, not seating, incorrectly adjusted, or the mixture screws are incorrectly adjusted.